Sara correctly find the volume of the square pyramid below to be 3534 ft³. What was the pyramid's height? 6 feet 19 feet

Answer 1

To find the height of the pyramid, we need to use the formula for the volume of a square pyramid:

Volume = (1/3) * base area * height

Given that the volume is 3534 ft³, we can set up the equation:

3534 = (1/3) * base area * height

Since the pyramid is a square pyramid, the base area is just the area of the square base:

Let x be the side length of the base.
The area of the square base is x².

Now we have:

3534 = (1/3) * x² * height

We also know that the base of the pyramid is a square with all sides equal. Since the base area is x², we also know that the base area must be equal to the square of one side of the base:

x² = (side length)²

Given that the volume is 3534 ft³, and using Sara's calculation, let's substitute the values back into the equation:

3534 = (1/3) * x² * height
3534 = (1/3) * 324 * height
3534 = 108 * height
height = 3534 / 108
height ≈ 32.72 feet

Therefore, the pyramid's height is approximately 32.72 feet.